Surface area rate

The surface area rate (or processing coefficient), relating the area irradiated per unit time to the beam current, and the absorbed dose is determined by measuring the surface dose at several beam current levels. 

Dehydration conditions Wt. loss (%) Surface area Rate constant" Glucose adsorbed... 

All physical and chemical transformations take time. Some physical phenomena, such as the vaporization at a boiling liquid surface, occurs very rapidly and for all practical purposes are instantaneous. Also, some chemical reactions, such as combustion reactions, are very rapid, but mass transfer and many chemical reactions are very slow by comparison. For such phenomena to occur to the extent desired requires allowing sufficient time, which is achieved by allowing sufficient equipment volume or surface area. Rate equations, then, are necessary to determine equipment sizes. For example, the well-known expression for the rate of heat transfer. 

Some authors (e.g., Helgeson et al., 1984 and Holdren and Speyer, 1987) consider S to be the reactive surface area and not the total surface area. This adjustment is made to account for preferential weathering at high energy sites on mineral surfaces that results in the creation of both reactive and nonreactive portions on mineral surfaces. Although it is theoretically and mechanistically interesting, the concept of reactive surface is of little practical importance because it is not possible to measure the reactive surface area. Rate constants can also be expressed in terms of mass of mineral, in which case, S in Eq. [2] is replaced by the mass. 

Figure 10. Arrhenius plots of oxygen isotope rate constants for select feldspar-salt solution (a) and clay/mica-fluid systems based on the simplified pseudo-first order surface area rate model (Eqn. 96).

Particle characteristics. Size and size distribution, porosity, degree of aggregation, specific surface area, rate of dissolution. 

Catalytic gas-phase reactions play an important role in many bulk chemical processes, such as in the production of methanol, ammonia, sulfuric acid, and nitric acid. In most processes, the effective area of the catalyst is critically important. Since these reactions take place at surfaces through processes of adsorption and desorption, any alteration of surface area naturally causes a change in the rate of reaction. Industrial catalysts are usually supported on porous materials, since this results in a much larger active area per unit of reactor volume. 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Tajima and co-workers [108] determined the surface excess of sodium dode-cyl sulfate by means of the radioactivity method, using tritiated surfactant of specific activity 9.16 Ci/mol. The area of solution exposed to the detector was 37.50 cm. In a particular experiment, it was found that with 1.0 x 10" Af surfactant the surface count rate was 17.0 x 10 counts per minute. Separate calibration showed that of this count was 14.5 X 10 came from underlying solution, the rest being surface excess. It was also determined that the counting efficiency for surface material was 1.1%. Calculate F for this solution. 

If the spreading is into a limited surface area, as in a laboratory experiment, the film front rather quickly reaches the boundaries of the trough. The film pressure at this stage is low, and the now essentially uniform film more slowly increases in v to the final equilibrium value. The rate of this second-stage process is mainly determined by the rate of release of material from the source, for example a crystal, and the surface concentration F [46]. Franses and co-workers [47] found that the rate of dissolution of hexadecanol particles sprinkled at the water surface controlled the increase in surface pressure here the slight solubility of hexadecanol in the bulk plays a role. 

The Washburn model is consistent with recent studies by Rye and co-workers of liquid flow in V-shaped grooves [49] however, the experiments are unable to distinguish between this and more sophisticated models. Equation XIII-8 is also used in studies of wicking. Wicking is the measurement of the rate of capillary rise in a porous medium to determine the average pore radius [50], surface area [51] or contact angle [52]. 

A rather different method from the preceding is that based on the rate of dissolving of a soluble material. At any given temperature, one expects the initial dissolving rate to be proportional to the surface area, and an experimental verification of this expectation has been made in the case of rock salt (see Refs. 26,27). Here, both forward and reverse rates are important, and the rate expressions are... 

Although the rate of dissolving measurements do thus give a quantity identified as the total surface area, this area must include that of a film whose thickness is on the order of a few micrometers but basically is rather indeterminate. Areas determined by this procedure thus will not include microscopic roughness (or fractal nature). 

Make a numerical estimate, with an explanation of the assumptions involved, of the specific surface area that would be found by (a) a rate of dissolving study, (b) Harkins and Jura, who find that at the adsorption of water vapor is 6.5 cm STP/g (and then proceed with a heat of immersion measurement), and (c) a measurement of the permeability to liquid flow through a compacted plug of the powder. 

Efficient use of a catalyst requires high rates of reaction per unit volume and, since reaction takes place on the surface of a solid, catalysts have high surface areas per unit volume. Therefore, tlie typical catalyst is porous, witli... 

Physical properties affecting catalyst perfoniiance include tlie surface area, pore volume and pore size distribution (section B1.26). These properties regulate tlie tradeoff between tlie rate of tlie catalytic reaction on tlie internal surface and tlie rate of transport (e.g., by diffusion) of tlie reactant molecules into tlie pores and tlie product molecules out of tlie pores tlie higher tlie internal area of tlie catalytic material per unit volume, tlie higher the rate of tlie reaction... 

Surface heterogeneity is difficult to remove from crystalline inorganic substances, such as metal oxides, without causing large loss of surface areas by sintering. Thus in Fig. 2.14 in which the adsorbent was rutile (TiO ) all three adsorbates show a continuous diminution in the heat of adsorption as the surface coverage increases, but with an accelerated rate of fall as monolayer completion is approached. 

From this equation we see that increasing k leads to a shorter analysis time. For this reason controlled-potential coulometry is carried out in small-volume electrochemical cells, using electrodes with large surface areas and with high stirring rates. A quantitative electrolysis typically requires approximately 30-60 min, although shorter or longer times are possible. 

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... 

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